As a consequence of the above construction, we see that there is a one-to-one correspondence between the vertexes of $\Pi$ and the components of the special fibre. For each $v\in\Pi^{0}$, the component $V(v)$ is a toric variety over $k$ defined by the fan $\Pi(v)$ in ${\widetilde{N}}_{\mathbb{R}}/\mathbb{R}(v,1)$. The orbits contained in $V(v)$ correspond to the polyhedra $\Lambda\in\Pi$ containing $v$. In particular, the components given by two vertexes $v,v^{\prime}\in\Pi^{0}$ share an orbit of dimension $l$ if and only if there exists a polyhedron of dimension $n-l$ containing both $v$ and $v^{\prime}$.